It is the aim of this paper to compute the next-to-next-to-next-to-leading
order (N\(^3\) LO) corrections of kinematic moments and assess their relevance
for the global fits of \(|V_{cb}|\) . Recently, we presented the N\(^3\) LO
corrections to the semileptonic width [1]} and the relation
between the on-shell and kinetic mass of the bottom
quark [2]}, [3]}. In these works we took advantage of
the heavy daughter expansion [4]} to determine finite charm
mass effects via an asymptotic expansion in the parameter
\(\delta = 1 -m_c/m_b\) , where \(m_c\)  and \(m_b\)  are the charm and bottom masses,
respectively. A similar strategy can be applied to compute moments in case no
experimental cuts are applied, i.e. moments of kinematic distributions
integrated over the whole phase space. We present in this work the first four
moments of the charged-lepton energy \(E_\ell \) , the total leptonic invariant
mass \(q^2\)  and the hadronic invariant mass \(M_X^2\) . We study the behaviour of
the perturbative series in the so-called kinetic scheme, in which the moments
are expressed in terms of the kinetic mass of the bottom quark
mass [5]}, [6]}, [2]}, [3]}.
Furthermore we estimate the theory uncertainty due to the finite expansion
depth in \(\delta \) .
